Entanglement network of the polypropylene/polyamide interface. 3. Deformation to fracture

Recently (Macromolecules 2000, 33, 1385, 1396), we have proposed a novel algorithm for generating entanglement network specimens of interfacial polymeric systems. The specimens are created by sampling the configurational distribution functions derived from a self-consistent mean field lattice model. Although overstretched strands can be relaxed by a Monte Carlo (MC) method, the specimens generated are not in detailed mechanical equilibrium. In this paper, we develop a method for relaxing the network with respect to its density distribution, and thereby imposing the condition of mechanical equilibrium, without changing the network topology. Our method rests on minimizing a free energy function characterizing the network, with respect to the coordinates of all entanglement points and chain ends. Contributions to the free energy include (a) the elastic energy due to stretching of the chain strands and (b) the free energy due to the repulsive and attractive (cohesive) interactions between segments. To calculate the interaction energy, a simple cubic grid is superimposed on the network. The repulsive interactions are calculated within each grid cell. The attractive interactions are calculated from contributions between cells and within each cell. We first apply the free energy minimization procedure to a simple system (bulk polypropylene) and obtain results which agree satisfactorily with experimental data and serve as a basis for parametrizing the interaction model. The free energy minimization is then applied to mechanically relax computer specimens of a polypropylene/polyamide6 (PP/PA6) interfacial system, strengthened by PP chains grafted onto the PA6 surface. The fully relaxed networks serve as a starting point for the mesoscopic simulation of fracture phenomena, caused by the application of tensile stress perpendicular to the interface. The network is deformed at a constant strain rate and the network topology evolves according to elementary mechanical processes of chain scission, chain slippage, disentanglement, and reentanglement. Chain slippage across an entanglement point occurs according to a Zhurkov activated rate equation with parameters derived from viscosity data. Each cycle of the kinetic MC algorithm used to track the deformation process consists of the imposition of a small incremental strain on the network, relaxation to mechanical equilibrium, introduction of the micromechanical processes mentioned above. and again relaxation to mechanical equilibrium. The MC cycles are repeated until fracture occurs. Results of the fracture experiments confirm the assertion, previously founded on structural grounds, that optimal adhesion in the PP/PA6 system examined is achieved for a relatively low surface grafting density of 0.1 chains/nm(2).